Unitarisability of discrete groups
Event details
| Date |
31.10.2018
|
| Hour |
15:00
› 16:00
|
| Speaker |
Maria Gerasimova (Dresden)
|
| Location |
|
| Category |
Conferences - Seminars |
- A group G is called unitarisable if every uniformly bounded representation of G in a Hilbert space can be conjugated to a unitary representation. It is well known that amenable groups are unitarisable. It has been open ever since whether this characterises the unitarisability of a group.
One of the approaches to study unitarisability is related to the space of Littlewood functions T1(G). We define the Littlewood exponent Lit(G) of a group G as follows:
Lit(G) = inf { p : T1(G) ⊆ lp(G) }.
On the one hand, Lit(G) is related to unitarisability and amenability and, on the other hand, it is related to some geometry of G or, more precisely, to the behavior of Cayley graphs when one increases the generating sets of G. We will discuss some applications of this connection.
We will also discuss the notion of p-isometrisability for uniformly bounded representations on p-spaces, which coincides with the usual unitarisability if p = 2. We will discuss examples of p-isometrisable groups and mention open questions and conjectures.
This is joint work with Dominik Gruber, Nicolas Monod and Andreas Thom.
Practical information
- General public
- Free
- This event is internal
